To add to User36303, you can do this easily online with Luigi1111's tool: http://xmr.llcoins.net/checktx.html. Just input a recipient address, a transaction ID, and a transaction key, and the tool will plug into the API of MoneroBlock.info and prove that a specific amount was sent.
Edit: Good followup by User36303 below. Luigi's tool is fine for casual confirmations, but for significant transaction confirmations a trustless independent analysis of the blockchain is probably the best first step, using the check_tx_key
command referenced above. Luigi's tool might be a decent second confirmation in these situations, however it entails a degradation of privacy since using it broadcasts your knowledge of the transaction to third parties.